Board members must act in the interest of shareholders, and that duty would keep them from approving Charter's offer because it undervalues the company, Marcus said Thursday on CNBC's "Squawk on the Street."

"The idea of waging a proxy fight here strikes me as a less-than-viable strategy," Marcus said. "I'm confident that [board members] would actually come to the same conclusion about the value that we can create versus what Charter is offering. I certainly do."

(Read more: Time Warner Cable lays out operating plan as it fends off takeover)

Charter offered $132.50 a share earlier this month, and Time Warner Cable countered by saying it would only consider a deal worth $160 per share. Marcus stood his ground on Thursday, but left open further talks.

Andrew Harrer | Bloomberg | Getty Images

Rob Marcus

"I want to be clear," he said. "It's not just the price but very explicit terms we put on the table. … We weren't just saying no. We were saying the offer that Charter made undervalued our company. But there was a price at which we would transact that we thought maximized value for the shareholder."

TWC posted better-than-expected quarterly earnings Thursday as the company tries to convince investors that it doesn't need Charter's help to orchestrate a turnaround. The cable and Internet provider has one of the worst customer service records among competitors, and subscribers have left the company in droves.

Marcus took over TWC as CEO at the beginning of 2014 after serving as COO.

In an interview with CNBC on Jan. 14, Charter CEO Tom Rutledge appealed directly to Time Warner Cable shareholders, and he didn't rule out trying to shake up the TWC board of directors in a proxy fight if leadership there continues to rebuff Charter's offers.

(Read more: Time Warner Cable customers may not see quick fix from merger)

Rutledge called his proposal a "rich and fair offer," and said TWC needs a significant investment to stage an "all-digital" turnaround and stem the tide of fleeing customers.

On Thursday, Marcus said TWC doesn't need Charter's help. The cable company picked up "quality" subscribers this month—TWC's best January in the past five years—he said, adding that he company remains on a "great trajectory" as it plans to improve high-speed data connections and reliability.

"There's no denying that 2013 was a rough year for us from a subscriber perspective," Marcus said. "The really good news is that we closed out the year with a tremendous amount of operating momentum."

—By CNBC's Jeff Morganteen. Follow him on Twitter at @jmorganteen and get the latest stories from "Squawk on the Street." Reuters contributed to this report.